Problem: Solve for $x$ and $y$ using substitution. ${-6x-y = -3}$ ${y = -5x+4}$
Solution: Since $y$ has already been solved for, substitute $-5x+4$ for $y$ in the first equation. ${-6x - }{(-5x+4)}{= -3}$ Simplify and solve for $x$ $-6x+5x - 4 = -3$ $-x-4 = -3$ $-x-4{+4} = -3{+4}$ $-x = 1$ $\dfrac{-x}{{-1}} = \dfrac{1}{{-1}}$ ${x = -1}$ Now that you know ${x = -1}$ , plug it back into $\thinspace {y = -5x+4}\thinspace$ to find $y$ ${y = -5}{(-1)}{ + 4}$ $y = 5 + 4$ $y = 9$ You can also plug ${x = -1}$ into $\thinspace {-6x-y = -3}\thinspace$ and get the same answer for $y$ : ${-6}{(-1)}{ - y = -3}$ ${y = 9}$